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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Generalized Bhaskar Rao Designs with Block Size 4 Signed over Elementary Abelian Groups

Gennian Ge1, Malcolm Greig2, Jennifer Seberry3
1Department of Mathematics, Suzhou University, Suzhou, 215006, P. R. China
2Greig Consulting, 317-130 East 11th St., North Vancouver, BC, Canada V7L 4R3
3School of Information Technology and Computer Science, University of Wollongong, Wollongong, NSW 2522, Australia.
  • Published: 31/08/2003

Abstract

De Launey and Seberry have looked at the existence of Generalized Bhaskar Rao designs with block size 4 signed over elementary Abelian groups and shown that the necessary conditions for the existence of a \( (v, 4, \lambda; EA(g)) \) GBRD are sufficient for \( \lambda > g \) with 70 possible basic exceptions. This article extends that work by reducing those possible exceptions to just a \( (9, 4, 18h; EA(9h)) \) GBRD, where \( \gcd(6, h) = 1 \), and shows that for \( \lambda = g \) the necessary conditions are sufficient for \( v > 46 \).

Keywords: Generalized Bhaskar Rao design, Group divisible design. AMS subject classification: 05B05.
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Citation
Gennian Ge, Malcolm Greig, Jennifer Seberry. Generalized Bhaskar Rao Designs with Block Size 4 Signed over Elementary Abelian Groups[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 046. 3-45. DOI: .